Semiparametric Dynamic Logit Model with Endogenous Networks

This paper develops identification and estimation methods for a semiparametric dynamic logit model in which a binary outcome depends on observed covariates, the lagged outcome, and an unknown function of a latent social characteristic that also governs the formation of social ties. The unobserved characteristic is allowed to vary across agents and over time, and the network formation process is left completely unspecified. Identification combines three elements: conditional likelihood arguments that exploit the logistic structure, network-type matching that eliminates the unknown social influence function by comparing agents whose observed linking behavior reveals identical latent characteristics, and local temporal smoothing that handles the interaction between dynamics and time-varying unobserved heterogeneity. A kernel-weighted conditional maximum likelihood estimator is proposed, and its consistency and asymptotic normality are established at the $\sqrt{n}$ rate. Monte Carlo simulations show that the estimator substantially reduces the bias present in naive and control-function approaches across a range of network formation models and achieves close to nominal coverage at moderate sample sizes. The method is applied to longitudinal data on adolescent smoking and friendship networks from the Glasgow Teenage Friends and Lifestyle Study. An extension to ordered outcomes is developed using composite conditional maximum likelihood.